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(7x-6)(2x+9)=0
We multiply parentheses ..
(+14x^2+63x-12x-54)=0
We get rid of parentheses
14x^2+63x-12x-54=0
We add all the numbers together, and all the variables
14x^2+51x-54=0
a = 14; b = 51; c = -54;
Δ = b2-4ac
Δ = 512-4·14·(-54)
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{5625}=75$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-75}{2*14}=\frac{-126}{28} =-4+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+75}{2*14}=\frac{24}{28} =6/7 $
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